ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Viscosity Sub-solutions in the Theory of M-hessian Equations


Nina Mihajlovna Ivochkina

Saint Petersburg State University
Professor of Department of Mathematical Physics
St. Petersburg, Peterhof, Universitetsky prospekt, 28
Professor. Doctor of Physical and Mathematical Sciences

Svetlana Ivanovna Prokof'eva

The St. Petersburg State University of Architecture and Civil Engineering
math. dept. Assoc.Prof.
St. Petersburg, 2-nd Krasnoarmeiskaia St. 4
Assoc.Prof. PhD in Physics and Mathematics

Galina Vladimirovna Yakunina

The St. Petersburg State University of Architecture and Civil Engineering
Associate Professor of Department of Mathematics
St. Petersburg, 2-nd Krasnoarmeiskaia St. 4
Assoc.Prof. PhD in Physics and Mathematics


We show that possible non-smoothness of viscosity sub-solutions is of no interest in the theory of m-Hessian operators. It is crucial that the set of viscosity C2-sub-solutions coincides with the set of correct setting of the Dirichlet problem. Moreover, we present an example to demonstrate that on the set of ellipticity of 5-Hessian operator the setting of the Dirichlet problem is incorrect because our problem has two infinitely differentiable solutions but only one of them is viscosity sub-solution.



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